Refers to a programming style that does not include any shortcuts to improve performance, but instead relies on sheer computing power to try all possibilities until the solution to a problem is found. A classic example is the traveling salesman problem (TSP). Suppose a salesman needs to visit 10 cities across the country. How does one determine the order in which cities should be visited such that the total distance traveled is minimized? The brute force solution is simply to calculate the total distance for every possible route and then select the shortest one. This is not particularly efficient because it is possible to eliminate many possible routes through clever algorithms.
Although brute force programming is not particularly elegant, it does have a legitimate place in software engineering. Since brute force methods always return the correct result -- albeit slowly -- they are useful for testing the accuracy of faster algorithms. In addition, sometimes a particular problem can be solved so quickly with a brute force method that it doesn't make sense to waste time devising a more elegant solution.
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